In recent years, there have been proposed and developed various vehicle dynamics control systems that control vehicle dynamic behavior concerned with the movements of automotive vehicles, such as acceleration, braking, and turning. In order to improve the vehicle stability, in particular the turning behavior, this type of vehicle dynamics control system often uses a yaw rate as a state variable of a turning behavior of a motor vehicle. For instance, when an oversteer tendency starts to develop on turns, a yawing moment by which the outward drift at the front of the vehicle occurs, is produced by applying a braking force to the outside front wheel in the turn. On the contrary, when an understeer tendency starts to develop on turns, a yawing moment by which the outward drift at the rear of the vehicle occurs, is produced by applying a braking force to the inside rear wheel in the turn. On four-wheel-drive-vehicles (4WDs) employing (i) a vehicle dynamics control system using a yaw rate as a state variable of a vehicle's turning behavior and (ii) a differential mechanism (such as a center differential) between front and rear wheel axles that permits the front axle to turn at a different speed than the rear axle while transmitting power from the propeller shaft to the front and rear wheel axles, suppose a braking force is applied to the outside front wheel in the turn so as to suppress oversteer tendencies during vehicle dynamics control. The outside front wheel in the turn, which is subjected to vehicle dynamics control, is hereinafter referred to as a “VDC controlled wheel”. If the braking force is applied to the VDC controlled wheel to suppress oversteer tendencies on turns and additionally the differential motion between front and rear wheel axles is limited by means of the differential mechanism, a braking force substantially corresponding to the braking force applied to the VDC controlled wheel is transferred from the VDC controlled wheel through the differential mechanism to each of rear wheels. Each road wheel, on which the transferred braking force acts, is hereinafter referred to as a “VDC noncontrolled wheel”. Owing to the transferred braking force, a lateral grip force of each VDC noncontrolled wheel (each rear wheel) on the road tends to reduce, thus undesirably increasing the oversteer tendency of yaw. In the same manner, suppose a braking force is applied to the inside rear wheel in the turn so as to suppress understeer tendencies during vehicle dynamics control. In this case, the inside rear wheel in the turn, which is subjected to vehicle dynamics control, is a “VDC controlled wheel”. If the braking force is applied to the VDC controlled wheel to suppress understeer tendencies on turns with the differential mechanism held in active operation, a braking force substantially corresponding to the braking force applied to the VDC controlled wheel is transferred from the VDC controlled wheel through the differential mechanism to each front wheel (each VDC noncontrolled wheel). Owing to the transferred braking force, a lateral grip force of each front wheel on the road tends to reduce, thus undesirably increasing the understeer tendency of yaw. Assuming that the driver depresses the brake pedal during vehicle dynamics control executed for suppressing oversteer or understeer tendencies on turns, there is an increased tendency for the lateral grip force of each of the aforementioned VDC noncontrolled wheels on the road to reduce due to the transferred braking force. To avoid this, Japanese Patent Provisional Publication No. 2000-344077 (hereinafter is referred to as “JP2000-344077”) corresponding to European Patent Application No. 1 059 216) has taught the inhibition of vehicle dynamics control (vehicle behavior control) or the braking force compensation at each individual wheel during vehicle dynamics control, when a differential motion between front and rear wheel axles is limited by a differential mechanism (e.g., with a central differential locked up).